Separating Covariate Shift from Mechanism Change with Two Discriminators

When labeled datasets differ, deciding what to inspect next requires separating a change in input frequencies from a change in the labeling rule. We develop a two-component diagnostic based on a balanced dataset source indicator $Z$: input information $I(Z;X)$ and conditional information $I(Z;Y\mid X)$, called conditional Jensen–Shannon discrepancy (CJSD). The components add to the joint Jensen–Shannon divergence. CJSD isolates label-rule differences on shared support, while the input component reveals how much conditional information remains observable. Two source classifiers estimate both components through held-out log losses, whose record-level differences connect a global score to regions worth inspecting. Controlled dataset pairs illustrate the separation and localize an imposed change in electricity records. Unaltered gas-sensor measurements demonstrate why a small conditional score can coexist with poor transfer when the inputs strongly separate. An equal-observation comparison with established conditional-information estimators assesses magnitude recovery, null behavior, and rotation sensitivity. Together, these results provide a practical way to read dataset differences and the limits of the evidence they supply.